吉 is not the object of 抜けちまう. の is a nominalizer, so さっさと抜けちまうの refers to an action "さっさと抜けちまう".I will pick up a good fortune?
That's because the meaning is different depending on the context. No one can answer your question "what 抜けちまう means" without knowing the context.I don't even know what 抜けちまう means here because of the different translations it has
The (batted) ball got past the first baseman.
When we emerged from the tunnel, we saw Mt. Fuji right in front of us.
The typhoon blew out into the Japan Sea.